# Asymptotic multivariate expectiles

## TL;DR

This paper studies the long-term behavior of multivariate expectiles, a type of risk measure, in different tail dependence scenarios, and proposes estimators for their asymptotic behavior.

## Contribution

It introduces estimators for multivariate expectiles' asymptotic behavior under various tail dependence conditions, expanding their applicability.

## Key findings

- Derived asymptotic properties of multivariate expectiles.
- Proposed estimators for asymptotic expectiles in different tail dependence cases.
- Analyzed behavior in Fréchet domain with asymptotic independence or comonotonicity.

## Abstract

In [16], a new family of vector-valued risk measures called multivariate expectiles is introduced. In this paper, we focus on the asymptotic behavior of these measures in a multivariate regular variations context. For models with equivalent tails, we propose an estimator of these multivariate asymptotic expectiles, in the Fr{\'e}chet attraction domain case, with asymptotic independence, or in the comonotonic case.